Elements of Geometry |
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Page 30
... radius CH pendicular to the chord MP , it will also be perpendicular to its parallel NQ ( 74 ) , and the point I will be at the same time the middle of the arc MHP and of NHQ ( 105 ) ; whence the arc MH = HP , and the arc NH = HQ ; also ...
... radius CH pendicular to the chord MP , it will also be perpendicular to its parallel NQ ( 74 ) , and the point I will be at the same time the middle of the arc MHP and of NHQ ( 105 ) ; whence the arc MH = HP , and the arc NH = HQ ; also ...
Page 31
... radius is less than the sum of the smaller and the distance of the centres , the two circles will cut each other . Demonstration . In order that the intersection may take place , the triangle ACD ( fig . 57 , 58 ) must be possible . It ...
... radius is less than the sum of the smaller and the distance of the centres , the two circles will cut each other . Demonstration . In order that the intersection may take place , the triangle ACD ( fig . 57 , 58 ) must be possible . It ...
Page 36
... radius greater than the half of AB , describe two arcs cutting each other in D ; the point D will be equally distant from the points A and B ; find , in like manner , either above or below the line AB , a second point E equally distant ...
... radius greater than the half of AB , describe two arcs cutting each other in D ; the point D will be equally distant from the points A and B ; find , in like manner , either above or below the line AB , a second point E equally distant ...
Page 37
... radius greater than BA , describe two arcs cutting each other in D ; draw AD , which will be the perpendicular required . For , the point D , being equally distant from B and C , must be in a perpendicular to the middle of BC ( 55 ) ...
... radius greater than BA , describe two arcs cutting each other in D ; draw AD , which will be the perpendicular required . For , the point D , being equally distant from B and C , must be in a perpendicular to the middle of BC ( 55 ) ...
Page 38
... radius equal to the chord LI , describe an arc cutting the arc BO in D ; draw AD , and the angle DAB will be equal to the given angle K. For the arcs BD , LI , have equal radii and equal chords ; they are therefore equal ( 102 ) , and ...
... radius equal to the chord LI , describe an arc cutting the arc BO in D ; draw AD , and the angle DAB will be equal to the given angle K. For the arcs BD , LI , have equal radii and equal chords ; they are therefore equal ( 102 ) , and ...
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Common terms and phrases
ABC fig adjacent angles altitude angle ACB angle BAC base ABCD bisect centre chord circ circular sector circumference circumscribed common cone consequently construction convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal angles equiangular equilateral equivalent faces figure formed four right angles frustum GEOM given point gles greater hence homologous sides hypothenuse inclination intersection isosceles triangle JOHN CRERAR LIBRARY join less Let ABC let fall line AC mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism produced proposition radii radius ratio rectangle regular polygon right angles Scholium sector segment semicircle semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three angles triangle ABC triangular prism triangular pyramids vertex vertices whence